NCERT Ganita Manjari, Class 9, textbook pages 123–164 (Part II)

How to help your child with Class 9 Maths Chapter 14, Math of Space: Surface Area and Volume, at home

Surface area and volume of solids, explained for parents: a 30-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

cylindercone = ⅓ cylinder

NCERT Class 9 Maths Chapter 14 Math of Space: Surface Area and Volume: what it teaches

Your teen finds surface areas and volumes of cuboids, cubes, cylinders, cones, pyramids, spheres and hemispheres, links formulas to nets, and applies them to tanks, cans and packaging.

Why it matters later. Surface area and volume continue in Class 10 with combinations of solids.

See it: this chapter in pictures

cube side 5 cmTSA = 6 × 25= 150 cm²
Six equal square faces.
cylinder r = 7, h = 10V = 22/7 × 49 × 10= 1540 cm³
Area of base × height.
sphere r = 7 cmV = 4/3 πr³≈ 1437 cm³
Cube the radius.

You need

  • boxes, cans, a ball
  • a ruler and measuring tape
  • a calculator

Tonight’s 30 minutes

  1. Open a box into its net and find its surface area.
  2. Measure a can: find its curved surface area (2πrh) and volume (πr²h).
  3. Fill a cone and a cylinder of the same base and height with rice: the cone holds a third.
  4. Find the volume of a ball of radius 7 cm (about 1437 cm³).

Words to use

  • surface area
  • volume
  • net
  • cylinder
  • cone
  • sphere
  • hemisphere

Watch for

  • Using diameter in place of radius. Halve the diameter first.
  • Mixing curved and total surface area. Total adds the flat faces.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouA cone and cylinder, same base and height: how many cones fill the cylinder?

Your childThree.

A game for this week: Container challenge

  1. Pick three containers at home.
  2. Estimate which holds most.
  3. Measure and calculate volumes.
  4. Check by pouring water.

A 5-day plan, 30 minutes a day

  1. Day 1Nets and surface area.
  2. Day 2Cylinder measurements.
  3. Day 3Cone vs cylinder.
  4. Day 4Spheres.
  5. Day 5Container challenge.

Everyday moments to practise

  • Water tanks.
  • Paint for walls.
  • Packaging design.
  • Ice-cream cones.

Quick check

Ask these at the end of the week. Tap to see the answer.

Volume of a cylinder r = 7 cm, h = 10 cm?

1540 cm³.

Cone vs cylinder of same base and height?

The cone has a third of the volume.

Surface area of a cube with side 5 cm?

150 cm².

Ready for the next chapter when your child…

  • Recalls surface area and volume formulas.
  • Chooses curved or total surface area correctly.
  • Solves real container problems.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Manjari (Class 9). See the full Class 9 parent guide for every chapter.

Questions parents ask

Why is a cone’s volume one third of a cylinder’s?

Experiments and calculus both show it; filling with rice demonstrates it.

What is the difference between CSA and TSA?

CSA is the curved part only; TSA includes flat faces.

Which π value to use?

As the question says: 22/7 or 3.14.